A complete season with attendance restrictions confirms the relevant contribution of spectators to home advantage and referee bias in association football.

Background: Due to the unfortunate pandemic situation, the phenomena of home advantage and referee bias in sports have recently received a particular research attention, especially in association football. In this regard, several studies were conducted on the last portion of the 2019-20 season: the majority of them suggests a reduction-but not the elimination-of the two phenomena, with some exceptions in which no reduction was found or, at the other extreme, the phenomena were not observed at all.

Methods: The continuation of the pandemic made it possible to replicate the previous studies considering the complete 2020-21 season, thus with the important added value of having a fully balanced home/away schedule-and a higher number of matches-in the various leagues. In particular, the sample of the present study consisted of 3,898 matches from the first and second divisions of the UEFA top five ranked countries, that is, England, Spain, Italy, Germany, and France. For the home advantage, the following variables were examined: distribution of matches outcomes and home advantage for points (also for previous seasons from the 2014-15 one); ball possession; total shots; shots on goal; and corner kicks. Instead, for he referee bias, the following variables were examined: fouls; yellow cards; red cards; penalty kicks; and extra time. Chi-square tests were used to compare the distribution of matches outcomes, and t-tests to compare home . away data for the other variables in the 2020-21 season; Bayesian and equivalence analyses were also conducted.

Results: The main results are as follows: (a) the distribution of matches outcomes in the 2020-21 season was significantly different from that of the last five complete seasons with spectators (Chi-square = 37.42, df = 2, < 0.001), with fewer home victories and more away victories; the resulting values of the home advantage for points were 54.95% for the 2020-21 season, and 59.36% for the previous seasons; (b) for the other home advantage variables, a statistically significant overall advantage for the home team emerged; nevertheless, the strength of the differences between home and away teams was generally small (0.09 < Cohen's < 0.17), and the corresponding means can be considered statistically equivalent for all variables but the total shots; (c) no statistically significant differences emerged between home and away teams for any of the referee bias variables.

Discussion: These findings demonstrate that the absence of spectators significantly reduced the home advantage compared to previous seasons with spectators. A slight home advantage persisted in the 2020-21 season, probably due to other factors, namely, learning and travel, according to the model by Courneya & Carron (1992). Conversely, the referee bias was not observed, suggesting that it mainly derives from the pressure normally exerted by spectators.